Algebra Examples

$\frac{1}{n - 10} \cdot \frac{n^{2} - 3 n - 70}{6 n^{2}}$

Step 1

Factor $n^{2} - 3 n - 70$ using the AC method.

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Step 1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 70$ and whose sum is $- 3$ .

$- 10, 7$

Step 1.2

Write the factored form using these integers.

$\frac{1}{n - 10} \cdot \frac{(n - 10) (n + 7)}{6 n^{2}}$

Step 2

Cancel the common factor of $n - 10$ .

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Step 2.1

Cancel the common factor.

$\frac{1}{n - 10} \cdot \frac{(n - 10) (n + 7)}{6 n^{2}}$

Step 2.2

Rewrite the expression.

$\frac{n + 7}{6 n^{2}}$